Digital communication systems transmit data by various carrier modulation techniques. The spectrum of a digital signal can be controlled and made compact by envelope filtering or phase domain filtering. Envelope filtering filters the baseband data stream prior to upconversion to the carrier frequency and power amplification. Envelope filtering for controlling out of band power of the transmitted signal, can be found in many operational communication systems. However, the power amplifier in the transmitter must be linearized or backed off to prevent spectral regrowth of the filtered signal. The more efficient phase domain filtering approach controls the signal spectrum by frequency modulating the filtered signal onto a carrier frequency to form a continuous phase modulated (CPM) signal. The CPM signal has a constant envelope so that the power amplifier can be operated at maximum output power without affecting the spectrum of the filtered signal.
Gaussian minimum shift keying (GMSK) is a form of continuous phase modulation having compact spectral occupancy by choosing a suitable bandwidth time product (BT) parameter in a Gaussian filter. The constant envelope makes GMSK compatible with nonlinear power amplifier operation without the concomitant spectral regrowth associated with non-constant envelope signals. These attributes render GMSK an attractive modulation scheme in all high throughput frequency division multiple access satellite communication systems where only a limited system bandwidth is available with the transmitters operating at maximum power output efficiency.
Data bits are formatted, for example, by non-return to zero (NRZ) formatting prior to Gaussian filtering, carrier modulation and power amplification. The formatted data is transmitted within data symbols of an M-ary alphabet of M possible data symbols. An M-ary GMSK signal is defined by the complex envelope described in terms of symbol energy E, symbol period T, carrier phase θc and phase pulse g(t) using a modulation index h and the equally probable NRZ data symbols belong to an M-ary alphabet. The GMSK phase pulse g(t) originates from a frequency response f(t) of the Gaussian smoothing filter with a single-sided 3 dB bandwidth B, time truncated to a time interval of LT, where L is an integer. For Gaussian filters with small BT products, the memory length L is approximately an integer greater than or equal to 1/BT. The length L is the number of elapsed symbol periods for the GMSK signal to accrue a full phase change due to a single input symbol and hence represents the memory of the GMSK signal. A GMSK signal with memory L greater than one is termed a partial response GMSK signal. The GMSK signal is communicated to a GMSK receiver subject to interference and additive white Gaussian noise (AWGN).
An optimum GMSK receiver for an additive white Gaussian noise channel demodulates the received signal by coherent demodulation into estimated output data stream using a local carrier reference. The receiver demodulates by filtering the received signal using a bank of Laurent filters that filter the demodulated received signal into a symbol sequence. A Viterbi decoder searches the symbol sequence for the most probable transmitted data sequence as an estimate of the original NRZ formatted data stream. A typical coherent receiver for 2-ary GMSK signal is based on a pulse amplitude modulation (PAM) representation of 2-ary CPM signals using Laurent matched filters matched to the amplitude modulated pulses in the PAM representation, and further employs the Viterbi algorithm to optimally demodulate the symbol sequence. For 2-ary GMSK transmitters with BT=¼ and with a channel Bit Error Rate (BER) of 0.01, or more, a GMSK receiver consisting of only two matched Laurent filters and a 4-state Viterbi algorithm can nearly achieve the performance of coherent binary phase shift Keying (BPSK) signaling communications. Amplitude modulated pulses have also been extended to PAM representation for 4-ary CPM signals.
In demodulating 2-ary and 4-ary GMSK signals using the Viterbi algorithm, a differential decoder is necessary to resolve data bit ambiguities while providing a degraded BER with respect to the absolute phase demodulation. It is desirable to reduce the BER. For noisy channels, the differential decoder yields poor bit error rate performance. The Viterbi algorithm typically employs a sliding window in the demodulation process where the width of the sliding window represents the demodulation memory or delay. The surviving state sequence Un=(Sn, Sn−1, . . . , Sn−w) produced by the sliding window Viterbi algorithm at any stage n depends on all the demodulated symbols {dk; 0≦k≦n} prior to that stage, where Sk=d0+d1+ . . . +dk. The term W is the size of the sliding window that is dictated by the memory length L of the underlying GMSK signal. This intrinsic data dependency of the survivor state sequences Un disadvantageously requires a differential decoder operation in the receiver when deciding on the actual demodulated symbol from successive survivors of the Viterbi algorithm resulting in a differential bit error rate (BER) degradation. These disadvantages are solved or reduced by the present invention.